Key Takeaways & Executive Findings
- •• A novel analytical model captures the full interaction between sequentially installed combined support systems and reinforced rock, incorporating elastic-brittle-plastic behavior and critical displacement transitions. • Virtual support pressure integrates the tunnel face spatial effect, enabling accurate prediction of ground characteristic curves under varied ground conditions. • The proposed method outperforms existing models and the convergence-confinement approach, as validated by numerical simulations and field measurements. • Key parameters—residual cohesion, friction angle of reinforced ground, and reinforcement thickness—significantly influence tunnel behavior; secondary support stiffness and installation timing critically affect support pressure.
Abstract
This study analyzed the interaction between sequentially installed combined support systems and the surrounding rock. Six distinct forms of elastic-brittle-plastic rock masses with reinforcement were analyzed, along with the critical displacements that governed their transition behaviors. Virtual support pressure was introduced to assess the spatial influence of the tunnel face. It was determined by integrating the longitudinal displacement profile with the proposed ground characteristic curve solutions under various ground conditions. Considering the timing of support installation, the support-rock interaction was divided into three phases. A method was presented to determine the evolution of this interaction based on critical displacements. An analytical approach was further proposed to describe the complete process of support system-rock interaction using displacement coordination. The analytical results are validated against numerical simulations and field measurements, and the method's advantages are demonstrated through comparisons with existing models and the convergence-confinement approach. Finally, the effects of surrounding rock and support parameters are examined. The results indicate that residual cohesion, the friction angle of reinforced ground, and reinforcement thickness strongly influence tunnel behavior. Additionally, increasing the stiffness or advancing the installation of secondary support substantially raises secondary support pressure.
1. Introduction
With the development of transportation infrastructure, tunnels constructed in complex surrounding rock conditions and high ground stresses are increasingly common. Such conditions often lead to construction challenges, including collapses, concrete cracking, and steel arch distortion [1−6]. To ensure construction safety, pre-reinforcement and combined support systems are widely implemented [7−10]. However, due to a lack of reliable calculation methods, empirical support design is commonly employed in practical engineering, leading to construction disasters in rock tunnels [11−13]. Therefore, a quantitative understanding of the combined support system-reinforced rock interaction is essential for the reliable design of the tunnel support system.
Traditional analyses of support-rock interaction typically consider a single uniform ground [14−17]. In such models, pre-reinforcement is either treated as whole-ground reinforcement or neglected entirely. In reality, the pre-reinforced region is limited and should be properly accounted for. To better evaluate its effect, it can be modeled as an equivalent circular region [18, 19]. Addressing reinforced ground displacement, FANG et al [20] developed a convergence-confinement approach (CCA), and SUN et al [21] later introduced an analytical model for primary support-surrounding rock interaction. However, these models assume that the rock mass behaves as elastic-perfectly-plastic (EPP), which fails to accurately capture the post-peak strength degradation of rock mass and may lead to dangerous calculation errors [22]. Furthermore, these studies focus only on a single primary support, lacking a comprehensive treatment of the interaction between combined support systems and reinforced rock.
During tunnel construction, multiple support systems are commonly employed. The primary support, typically consisting of shotcrete and steel arches, is installed immediately after excavation. In soft rock tunnels, multiple steel arches combined with shotcrete are often used, requiring sequential supports to act synergistically to ensure tunnel safety. For tunnels with standard composite linings, which include both primary support and secondary lining, the secondary lining is installed to guarantee long-term stability [23]. In this case, the installation time and stiffness of secondary lining are critical design factors. Ensuring tunnel safety requires a thorough investigation of the combined support system-surrounding rock interaction. WU et al [24] analyzed tunnel displacement and stress conditions under double primary supports and evaluated their feasibility. TAN et al [25], and GUO et al [26] utilized on-site displacement monitoring, displacement rate analysis, and structural safety factor evaluation.
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CHEN Xu, ZHANG Ding-li, SUN Zhen-yu, CHEN Xuan-hao (2026). Interaction analysis of sequentially installed support system and reinforced rock for deep tunnels. Journal of Central South University. https://doi.org/10.1007/s11771-026-6194-5
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Frequently Asked Questions
What is the main contribution of this paper?
The paper presents a novel analytical model that comprehensively analyzes the interaction between sequentially installed combined support systems and reinforced rock in deep tunnels, incorporating elastic-brittle-plastic behavior and critical displacement transitions, and validated against numerical and field data.
How does the proposed method improve upon existing approaches?
Unlike traditional models that assume elastic-perfectly-plastic behavior and consider only single support, this method accounts for post-peak strength degradation, sequential support installation, and the spatial effect of the tunnel face via virtual support pressure, leading to more accurate predictions.
What are the key parameters affecting tunnel behavior according to the study?
Residual cohesion, friction angle of reinforced ground, and reinforcement thickness significantly influence tunnel behavior. Additionally, increasing the stiffness or advancing the installation of secondary support substantially raises secondary support pressure.
How is the analytical model validated?
The analytical results are validated against numerical simulations and field measurements, and the method's advantages are demonstrated through comparisons with existing models and the convergence-confinement approach.
What practical implications does this research have for tunnel engineering?
The findings provide a quantitative basis for designing combined support systems in deep tunnels, helping engineers optimize support installation timing and stiffness to ensure safety and stability.
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